Prospects for Applied Mathematics and Data Analysis

Journal DOI

https://doi.org/10.54216/PAMDA

Submit Your Paper

2836-4449ISSN (Online)

Volume 1 , Issue 2 , PP: 08-16, 2023 | Cite this article as | XML | Html | PDF | Full Length Article

Infra bi-Topological space

Riad K. Al-Hamido 1 *

  • 1 Department of Mathematics, College of Science, AlFurat University, Deir-ez-Zor, Syria - (riad-hamido1983@hotmail.com)
  • Doi: https://doi.org/10.54216/PAMDA.010201

    Received: August 18, 2022 Accepted: December 17, 2022
    Abstract

    In this paper, we introduce infra bi-topological structure which is a more general structure than infra-topological spaces. This new space make us enable to increate a new sub-classes of sets, called  infra bi-open (bi-closed) sets,  pairwise infra-open (closed) sets. also we define infra bi-closure, pairwise infra bi-interior and their basic properties are presented. The relations of these concepts with their counterparts in infra-topological space s are given and many examples are presented.

    Keywords :

    Infra bi-topological spaces , pairwise infra-open (closed) sets , infra bi-open  , (bi-closed) sets.

    References

    A.  M.  AL-Odhari,  On  infra  topological  space,  International  Journal  of  Mathematical  Archive, 

    (2015), 6(11), 179-184.

    [2]  J. C. Kelly. Bitopological spaces. Proceedings of the London Mathematical Society,(1963), 3(1), 71 -89.

    [3]  R. Gowri, A.K.R. Rajayal, On Supra Bi-Topological space4s, IOSR Journal of Mathematics (IOSRJM) .No.5(113)(2017),55-58.

    [4]  S. Mashhour, A.A. Allam, F.S. Mahmoud and F.H. Khedr, On Supra topological spaces, Indian Jr.Pure 

    and Appl.Math.No.4(14)(1983),502-510.

    [5]  L. A. Zadeh. Fuzzy Sets. Inform. Control, (1965),8, 338-353.

    [6]  F.  Smarandache,  “Neutrosophy  and  Neutrosophic  Logic,  First  International  Conference  on 

    Neutrosophy, Neutrosophic Logic, Set, Probability, and Statistics” University of New Mexico, Gallup, 

    NM 87301, USA (2002).

    A.  A  Salama;  F.Smarandache  and  Kroumov.  “Neutrosophic  crisp  Sets  and  Neutrosophic  crisp 

    Topological Spaces” Neutrosophic Sets and Systems, Vlo.2, (2014), pp.25-30.

    B.  A. Salama and S. A. Alblowi. Neutrosophic set and neutrosophic topological space. ISORJ, 

    Mathematics, Vol. (3), Issue 4, ( 2012), 31-35.

    [7]  Mashhour, S.; Allam, A.A.; Mahmoud  F.S.; and Khedr, F.H.; On Supra topological spaces”, Indian 

    Jr.Pure and Appl.Math.No.4(14)(1983),502-510.

    [8]  R.K.  Al-Hamido.  “A  study  of  multi-Topological  Spaces”,  PhD  Theses  ,AlBaath  university  , 

    Syria(2019).

    A.  S. Mashhour, A. A. Allam, F. S. Mahmoud, and F. H. Kheder, “On supra topological spaces,”

    Indian Journal of Pure and Applied Mathematics, vol. 14, pp. 502–510, 1983.

    [9]  T.  Al-Shami,  “Some  results  related  to  supra  topological  spaces,”  Journal  of  Advanced  Studies  in 

    Topology, vol. 7, no. 4, pp. 283–294, 2016.

    [10]  R.  Devi,  S.  Sampathkumar,  and  M.  Caldas,  “On  α-open  sets  and  sα-continuous  maps,”  General 

    Mathematics, vol. 16, pp. 77–84, 2008.

    [11]  O.  R.  Sayed,  “Supra  pre-open  sets  and  supra  pre-continuous  on  topological  spaces,”  Series 

    Mathematics and Information, vol. 20, pp. 79–88, 2010.

    [12]  O.  R.  Sayed  and  T.  Noiri,  “On  supra  b-open  sets  and  supra  bcontinuity  on  topological  spaces,”

    European Journal of Pure and Applied Mathematics, vol. 3, pp. 295–302, 2010.

    [13]  S. Jafari and S. Tahiliani,  “Supra  β-open sets and supra  β-continuity on topological spaces,”  Annales 

    Universitatis Scientiarium Budapestinensis, vol. 56, pp. 1–9, 2013.

    [14]  M.  E.  El-Shafei,  M.  Abo-Elhamayel,  and  T.  M.  Al-Shami,  “On  supra  R-open  sets  and  some 

    applications on topological spaces,” Journal of Progressive Research in Mathematics, vol. 8, pp. 1237 –

    1248, 2016.

    [15]  T.  Al-Shami,  “On  supra  semi  open  sets  and  some  applications  on  topological  spaces,”  Journal  of 

    Advanced Studies in Topology, vol. 8, no. 2, pp. 144–153, 2017. T. M.  Al-Shami, “Utilizing supra α-open  sets  to  generate  new  types  of  supra  compact  and  supra  lindel¨of  spaces,”  Facta  Universitatis, 

    Series: Mathematics and Informatics, vol. 32, pp. 151–162, 2017. 

    [16]  T. M. Al-Shami, “Supra semi-compactness via supra topological spaces,” Journal of Taibah University 

    for Science, vol. 12, no. 3, pp. 338–343, 2018. 

    [17]  T. M. Al-Shami,  B.  A. Asaad, and M. A. El-Gayar,  “Various types of supra pre-compact and supra 

    pre-Lindel¨of spaces,”Missouri Journal of Mathematical Science, vol. 32, 2020.

    [18]  J.  M.  Mustafa,  “Supra  b-compact  and  supra  b-Lindelof  spaces,”  Journal  of  Mathematics  and 

    Applictions, vol. 36, pp. 79–83, 2013.

    [19]  G.Jayaparthasarathy;  V.F.Little  Flower;  M.Arockia  Dasan.  “Neutrosophic  Supra  Topological 

    Applications in Data Mining Process”, Neutrosophic Sets and Systems, ,(2019) ,vol. 27, pp. 80 -97.

    A.  B.AL-Nafee;  R.K.  Al-Hamido;  F.Smarandache.  “Separation  Axioms  In  Neutrosophic  Crisp 

    Topological Spaces”,Journal of newtheory, (2018),vol. 22, pp.

    [20]  R. Gowri, A.K.R. Rajayal, “On Supra Bi-topological spaces”, IOSR Journal of Mathematics (IOSRJM) .No.5(113)(2017),55-58.

    [21]  J. C. Kelly.  “Bi-topological spaces”. Proceedings of the London Mathematical Society, 3(1) ,(1963), 

    71-89.

    [22]  T.Y. Ozturk , A. Ozkan “Neutrosophic Bi-topological Spaces”, Neutrosophic Sets and Systems, vol. 

    30,(2019) ,pp. 88-97.

    [23]  R.K. Al-Hamido. “Neutrosophic Crisp Bi-Topological Spaces”, Neutrosophic Sets and Systems, vol. 

    21, (2018), pp. 66-73. 

    [24]  M.  Parimala,  M.  Karthika  ,F.  Smarandache.  “Introduction  to  neutrosophic  minimal  structure”, 

    Neutrosophic Sets and Systems, vol. 36, (2020) , pp. 376-388. 

    [25]  R. K. Al-Hamido, On Neutrosophic Tri-Topological space, (2018). Journal of newtheory, vol. 23, pp. 

    13-21. 

    [26]  R.K. Al-Hamido, Q. H. Imran, K. A. Alghurabi, T. Gharibah, “On Neutrosophic Crisp  Semi Alpha 

    Closed Sets”, Neutrosophic Sets and Systems”, vol. 21, 28-35, (2018). 

    [27]  Q. H. Imran, F. Smarandache, R.K. Al-Hamido, R. Dhavasselan, “On Neutrosophic Semi Alpha open 

    Sets”, Neutrosophic Sets and Systems, vol. 18, 37-42, (2017).

    [28]  R.K.  Al-Hamido,  T.  Gharibah,  S.  Jafari  F.Smarandache,  “On  Neutrosophic  Crisp  Topology  via  NTopology”, Neutrosophic Sets and Systems, vol. 21, 96-109, (2018). 

    [29]  F.  Smarandache,  A  Unifying  Field  in  Logics:  Neutrosophic  Logic.  Neutrosophy,  Neutrosophic  Set, 

    Neutrosophic Probability. American Research Press, Rehoboth, NM, (1999).

    [30]  F.  Smarandache,  Neutrosophy  and  Neutrosophic  Logic,  First  International  Conference  on 

    Neutrosophy, Neutrosophic Logic, Set, Probability, and Statistics, University of New Mexico, Gallup, 

    NM 87301, USA (2002).

    A.  A.Salma,  S.A.  Alblowi,.  Neutrosophic  set  and  neutrosophic  topological  spaces.  IOSR  J. 

     

    Math., (2012) 3(4), 31–35.

    Cite This Article As :
    K., Riad. Infra bi-Topological space. Prospects for Applied Mathematics and Data Analysis, vol. , no. , 2023, pp. 08-16. DOI: https://doi.org/10.54216/PAMDA.010201
    K., R. (2023). Infra bi-Topological space. Prospects for Applied Mathematics and Data Analysis, (), 08-16. DOI: https://doi.org/10.54216/PAMDA.010201
    K., Riad. Infra bi-Topological space. Prospects for Applied Mathematics and Data Analysis , no. (2023): 08-16. DOI: https://doi.org/10.54216/PAMDA.010201
    K., R. (2023) . Infra bi-Topological space. Prospects for Applied Mathematics and Data Analysis , () , 08-16 . DOI: https://doi.org/10.54216/PAMDA.010201
    K. R. [2023]. Infra bi-Topological space. Prospects for Applied Mathematics and Data Analysis. (): 08-16. DOI: https://doi.org/10.54216/PAMDA.010201
    K., R. "Infra bi-Topological space," Prospects for Applied Mathematics and Data Analysis, vol. , no. , pp. 08-16, 2023. DOI: https://doi.org/10.54216/PAMDA.010201